Warm the olive oil in a large stockpot or Dutch oven set over medium heat. Once hot, add the chopped onion, minced garlic, and crushed red pepper flakes. Sauté the mixture gently for 3 to 4 minutes, or until the onion becomes translucent and the garlic is fragrant but not browned.
Carefully place the smoked turkey wing into the pot along with the water. Cover with a lid and bring the liquid to a rolling boil. Once boiling, reduce the heat to a low simmer and cook—still covered—for 1 hour. This will infuse the broth with deep, smoky flavor.
Remove the turkey wing and transfer it to a cutting board. Let it rest and cool slightly for about 5 to 10 minutes.
While the turkey is cooling, stir in the chopped collard greens. Push them down gently with a spoon to help them wilt and submerge into the broth. Allow the greens to simmer uncovered for 45 to 60 minutes, or until they reach a silky, tender consistency.
Meanwhile, strip the meat from the cooled turkey wing, discarding the skin. Add both the meat and the bones back into the pot, returning all that flavor to the simmering greens.
In the final minute of cooking, mix in the apple cider vinegar, sugar, and kosher salt. Stir well to ensure the sugar dissolves fully and the seasoning is evenly distributed.
To serve, use a slotted spoon to lift the greens into a serving bowl. Ladle the flavorful cooking liquid—known as potlikker—into a separate dish for dipping cornbread or sipping alongside your meal.